Oceanographers use submerged sonar systems, towed by a cable from a ship, to map the ocean floor. In addition to their downward

Answer:

Explanation:

According to the parameters provided,

mass of the clay lump, m₁ = 0.05 kg

initial velocity of the lump, u₁ = 12 m/s

mass of the cart, m₂ = 0.15 kg

initial speed of the cart, u₂ = 0

As the clay adheres to the cart, we have an inelastic collision scenario. Let v represent the combined speed of both the cart and lump post-collision. Given that momentum is conserved, we have:

The resultant speed is v = 3 m/s.

Thus, the final speed of both cart and lump following the collision is 3 m/s. This concludes the solution.

Answer:

a) factor

b) factor

c) factor

d) factor

Explanation:

For an oscillating spring-mass system, the time period is expressed as:

where:

represents the frequency of oscillation

signifies the mass linked to the spring

is the spring's stiffness constant

a) If the mass is doubled:

• New mass,

Thus, the new time period:

this leads to factor as per the question.

b) When the stiffness constant is quadrupled, holding other factors constant:

New stiffness constant,

Thus, the new time period:

this results in factor as required.

c) When both mass and stiffness constant are quadrupled:

New stiffness,

New mass,

Thus, the new time period:

which leads to factor as stated in the question.

d) If amplitude is quadrupled, the time period remains unaffected because T does not depend on amplitude as demonstrated by the equation.

Thus, factor